The thermodynamic properties of a $d$ -dimensional classical vector-spin system in a random magnetic field are calculated explicitly in the spherical-model limit. The system is characterized by significant spin-glass order of the Edwards-Anderson type even when no transition to a state with spontaneous magnetization occurs. This spin-glass order should result in observable effects in the magnetic susceptibility and specific heat. The properties of the random-field spherical model are compared with those reported for the corresponding Ising model. The behavior of the coherence length is identical in both models at their respective lower critical dimensionalities.The thermodynamic properties of a $d$-dimensional classical vector-spin system in a random magnetic field are calculated explicitly in the spherical-model limit. The system is characterized by significant spin-glass order of the Edwards-Anderson type even when no transition to a state with spontaneous magnetization occurs. This spin-glass order should result in observable effects in the magnetic susceptibility and specific heat. The properties of the random-field spherical model are compared with those reported for the corresponding Ising model. The behavior of the coherence length is identical in both models at their respective lower critical dimensionalities.

Physical review. B, Condensed matterOct 1, 198235 citations

The fully finite spherical model

Jonathan Shapiro, Joseph Rudnick

Journal of Statistical PhysicsApr 1, 198635 citations

Critical behavior of a quantum spherical model in a random field

Thomas Vojta, Michael Schreiber

We consider the influence of a quenched random field on the critical behavior of a quantum spherical model at the zero-temperature quantum phase transition. We find a complete solution of the model for arbitrary translationally invariant pair interactions. It turns out that the critical behavior for zero as well as finite temperatures is dominated by static random field fluctuations rather than by quantum or thermal fluctuations. Therefore the critical behavior close to the zero-temperature quantum phase transition is identical to that close to a finite-temperature transition. The system does not show a crossover from quantum to classical behavior. \textcopyright{} 1996 The American Physical Society.We consider the influence of a quenched random field on the critical behavior of a quantum spherical model at the zero-temperature quantum phase transition. We find a complete solution of the model for arbitrary translationally invariant pair interactions. It turns out that the critical behavior for zero as well as finite temperatures is dominated by static random field fluctuations rather than by quantum or thermal fluctuations. Therefore the critical behavior close to the zero-temperature quantum phase transition is identical to that close to a finite-temperature transition. The system does not show a crossover from quantum to classical behavior. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterApr 1, 199626 citations

Critical behavior of the stochastic spherical model

Masuo Suzuki

Physics Letters AMar 1, 197315 citations

Spherical random-field systems with long-range interactions: general results and application to the Coulomb glass

Thomas Vojta

A classical spherical random-field Hamiltonian with long-range (power-law) interactions is investigated by means of the replica theory. Both ferromagnetic and anti-ferromagnetic interactions are considered. The use of continuous variables instead of Ising variables in the spherical version of the model allows one to calculate the free energy exactly. The existence of an equilibrium phase transition is investigated based on the replica-symmetric solution. The results are applied to the Coulomb-glass model of interacting localized electrons in a disordered solid. This model is shown not to have an equilibrium phase transition for spatial dimensions D<or=4. For D>4 the model has a phase transition to an ordered phase; however, it does not have a phase transition to a 'glassy' phase.A classical spherical random-field Hamiltonian with long-range (power-law) interactions is investigated by means of the replica theory. Both ferromagnetic and anti-ferromagnetic interactions are considered. The use of continuous variables instead of Ising variables in the spherical version of the model allows one to calculate the free energy exactly. The existence of an equilibrium phase transition is investigated based on the replica-symmetric solution. The results are applied to the Coulomb-glass model of interacting localized electrons in a disordered solid. This model is shown not to have an equilibrium phase transition for spatial dimensions D<or=4. For D>4 the model has a phase transition to an ordered phase; however, it does not have a phase transition to a 'glassy' phase.

Journal of Physics A Mathematical and GeneralJun 21, 199323 citations

The thermodynamic properties of a

d

-dimensional classical vector-spin system in a random magnetic field are calculated explicitly in the spherical-model limit. The system is characterized by significant spin-glass order of the Edwards-Anderson type even when no transition to a state with spontaneous magnetization occurs. This spin-glass order should result in observable effects in the magnetic susceptibility and specific heat. The properties of the random-field spherical model are compared with those reported for the corresponding Ising model. The behavior of the coherence length is identical in both models at their respective lower critical dimensionalities.